Storms of 185 mph winds have attained what should be labeled Category 6. The gusts of 220 mph have attained what should be Category 7.
Hurricane Wind Strength Increases as the Square of the Velocity
We show the relative force strengths associated with the velocities starting the various category storms, and with the very high velocity of Hurricane Dorian. Part of this is copied from my article two years ago when it was applied to Hurricane Irma, which also had 185 mph sustained winds.
Force is generated by the change in momentum of the striking air in a unit time. The Force on a unit area is the momentum hitting it for density r and mass m, with velocity V, which is m X V in a unit time. But in a unit time, a horizontal column of length V, hits, with mass m = r X V. Substituting that for m gives F = r V^2. That is that the force per unit area or pressure is the density times the velocity squared. The relative situation is when a car is speeding through the air, the car hits the air, and the force of air friction goes as velocity squared.
In terms of pressure to lift roofs or objects, the Bernoulli equation shows that the pressure drop in gasses or fluids flowing over objects also is proportional to the density times the velocity squared. This effect can lift roofs off, and also flowing around the sides of buildings can rip out walls and windows. Some houses were tall and narrow, and were easy targets to be tipped over.
The ideal gas law: PV = kNT has the pressure P proportional to the number of gas molecules N, and the Temperature, where the kinetic energy per molecule is
1/2 m v^2 = kT. V here is just the fixed volume, and v is the velocity.
We will give a table of the minimum velocity of each hurricane category of the Sappir-Simpson scale, the minimum velocity of each category, and then the velocity scaled by 100 mph and then squared for a relative measure. The last column scales the minimum velocities by that for Category 1, V1.
Category. Minimum Velocity. V^2/100^2 (V/V1)^2
- 74 mph. 0.55. 1.00
2. 96 mph. 0.92 1.68
3. 111 mph 1.23 2.25
4. 130 mph. 1.69 3.09
5. 157 mph. 2.46 4.50
(6) Dorian 185 mph. 3.42 6.25
(7) Gusts 220 mph 4.84 8.83
Note that a category 5 at minimum is twice the force of a category 3 at minimum. A category 3 at minimum is 2.2 times a category 1 at minimum. Since Dorian’s and Irma’s velocity squared at its 185 mph maximum of 3.42 is twice the category 4 value of 1.69, it would have achieved Category 6, if their was one. The largest hurricanes have topped off at 185 or 186 mph. Calling Dorian a Category 5 ignores the fact that its wind pressure is 3.42/2.46 = 1.39, or 39%, or almost 40% greater than the start of Category 5.
One problem with using the scale on a map, is that right after the storm changes from 5 to 4, it is still close to a 5, yet could mislead viewers to think that it has sunk to the base of a 4. CNN is now showing a sliding scale to prevent this problem. It could also be solved by using a 4.5 or 4-5 label. Right now, Dorian is labeled as a Category 4 on the CNN headline, but the 155 mph winds are just slightly under Category 5.
Below the hurricane scale is a tropical storm which starts at 39 mph to 73 mph. 39 mph scaled by 100 mph give a comparative entry for V^2/100^2 of 0.15.
The wind speed is the average over a minute at ground level at the eyewall of the hurricane.
The Catagory is determined by the maximum wind which occurs at tha edge of the eyewall. The width of the Irma storm is an incredible 370 miles. The radii where Dorian started with Category 1 winds is 45 miles from the center, and tropical storm-force winds is 140 miles outward. The radii where Irma started with Category 1 or hurricane force winds in the four different directions was 57, 57, 52, and 40 miles from the center.
Dorian’s pressure got down to a low of 910 millibars. Normal atmospheric pressure is about 1,000 millibars. Here is the CNN historical record of the lowest pressure of Atlantic Hurricanes. Unfortunately, it labels Dorian as a CAT 5, not a CAT 6.
With Dorian, while the wind speed average was 185 mph, the wind gusts went up to 220 mph. Clearly the gusts could cause the worst damage. However, one commentator pointed out that the continued rattling of the steady wind causes the damage. Scaling 220 mph by 100 mph and squaring gives the relative V^2/100^2 of 4.84. Scaling it by V1 of 74 mph squared gives 8.83. Even though 160 mph is at the start of category 5, the gusts increased the force by 97%, or a factor of 2. This means that the gusts were actually Category 7!
With the storm Irma in 2017, CNN also gave an example of how the wind speed increases as you go up higher in a building. We give a short table of different floor heights, wind speed in the example, and velocity scales by 100 mph squared. The 145 mph is the expected wind speed from Irma in Miami.
Level. Velocity. V^2/100^2 (V/V1)^2
Ground. 145 mph 2.10 3.84
30 story. 174 mph. 3.03 5.53
80-100 story. 189 mph. 3.57 6.52
This says that if the wind velocity at the ground is midway between category 4 and 5, at a very tall building it would be at a Category 6 value. The rule that they use is that the wind speed increases 20% above the ground speed at 30 stories, and 30% above the ground speed at 80-100 stories. In terms of the force or V^2, that increases by 44% at 30 stories, and 69% at 80-100 stories.
It seems that the higher force acting on the water will also increase waves and storm surge. The problem is, that waves and storm surge do not dissipate easily, but build up as the hurricane lingers.
These are CNN’s statements on how climate change is making Hurricanes more dangerous.
Freeport, Bahamas is about 100 miles from ports at Miami and Fort Lauderdale. Isn’t it about time that we offered them federal aid, in addition to the generous charitable aid being organized? Very likely the presence of the Bahamas also contributes to the tourist income of Florida.
